its been years since i have done it personally, maybe it was 2014-2015

but from /r/dogecoin

https://www.reddit.com/r/dogecoin/comments/1x6xvp/how_do_i_find_my_private_key/

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click on 'help' in the menu bar (top right)

click on 'debug window'

select the 'console' tab

*type: walletpassphrase "your walletpassphrase here"

type: dumpprivkey [your public key here]

this will return the private key, you can copy it now; ensure you clear your clipboard/history afterwards

*type: walletlock

* ignore these steps if your wallet isn't encrypted.